本論文討論太陽能飛行載具的最佳垂直爬升飛行軌跡，太陽能飛行載具飛行時，質量一直維持定值，與以往針對燃油消耗率所研究之最佳飛行軌跡不同。為簡化問題，考慮載具飛行於平坦地球表面之數學模型，利用最佳化理論中Pontryagin最小化原理得到一組包含運動方程式及附屬變數 (costate variables)方程式的邊界值微分方程式。其中，有些初始條件未知，因此利用射擊法來求得最佳爬升軌跡。 根據最佳化理論，對於不限定最終時間的問題， 除了要滿足邊界條件外，Hamiltonian也必須同時為零。但是，在經過很多方法的嘗試，僅能得到符合邊界條件，但是Hamiltonian不為零的軌跡。因此，本文的結果還不能稱為最佳爬升軌跡。本文列出所有的嘗試，期能參考本文中的經驗找出更好的方法，進而找出符合最佳化理論的最佳爬升軌跡。 The thesis studies the optimal climb trajectory for the solar powered aerial vehicle. Since the solar powered vehicle doesn’t expel the fuel, the mass of the vehicle keeps in constant during the flight. For the optimal trajectory, the energy expense is the cost function. To find the optimal climbing trajectory, we shall use the Pontryagin theory to form a set of differential equations which consists of the equations of motion and the ajoint equations with given boundary values. We use the shooting method to solve the boundary value problem. By the Pontryagin theory, the optimal climb trajectory is achieved when not only the boundary values are satisfied but also the Hamitonian equals zero for the free final time problem. However after many attempts, the study doesn’t obtain a trajectory with Hamiltonian equals zero while the boundary values are satisfied. Although the study doesn’t find the optimal climbing trajectory, the attempts and the associated observations are listed in the thesis for the further researches.
